Rheometry of granular materials in cylindrical Couette cells: Anomalous stress caused by gravity and shear

The cylindrical Couette device is commonly employed to study the rheology of fluids, but seldom used for dense granular materials. Plasticity theories used for granular flows predict a stress field that is independent of the shear rate, but otherwise similar to that in fluids. In this paper we report detailed measurements of the stress as a function of depth, and show that the stress profile differs fundamentally from that of fluids, from the predictions of plasticity theories, and from intuitive expectation. In the static state, a part of the weight of the material is transferred to the walls by a downward vertical shear stress, bringing about the well-known Janssen saturation of the stress in vertical columns. When the material is sheared, the vertical shear stress changes sign, and the magnitudes of all components of the stress rise rapidly with depth. These qualitative features are preserved over a range of the Couette gap and shear rate, for smooth and rough walls and two model granular materials. To explain the anomalous rheological response, we consider some hypotheses that seem plausibleapriori, but showthat none survive after careful analysis of the experimental observations. We argue that the anomalous stress is due to an anisotropic fabric caused by the combined actions of gravity, shear, and frictional walls, for which we present indirect evidence from our experiments. A general theoretical framework for anisotropic plasticity is then presented. The detailed mechanics of how an anisotropic fabric is brought about by the above-mentioned factors is not clear, and promises to be a challenging problem for future investigations. (C) 2013 AIP Publishing LLC.

Analysis of shear bands in slow granular flows using a frictional Cosserat model

The slow flow of granular materials is often marked by the existence of narrow shear layers, adjacent to large regions that suffer little or no deformation. This behaviour, in the regime where shear stress is generated primarily by the frictional interactions between grains, has so far eluded theoretical description. In this paper, we present a rigid-plastic frictional Cosserat model that captures thin shear layers by incorporating a microscopic length scale. We treat the granular medium as a Cosserat continuum, which allows the existence of localised couple stresses and, therefore, the possibility of an asymmetric stress tensor. In addition, the local rotation is an independent field variable and is not necessarily equal to the vorticity. The angular momentum balance, which is implicitly satisfied for a classical continuum, must now be solved in conjunction with the linear momentum balances. We extend the critical state model, used in soil plasticity, for a Cosserat continuum and obtain predictions for flow in plane and cylindrical Couette devices. The velocity profile predicted by our model is in qualitative agreement with available experimental data. In addition, our model can predict scaling laws for the shear layer thickness as a function of the Couette gap, which must be verified in future experiments. Most significantly, our model can determine the velocity field in viscometric flows, which classical plasticity-based model cannot.

Unsteady-Flow Of A Viscous-Fluid Between 2 Parallel Disks With A Time-Varying Gap Width And A Magnetic-Field

The unsteady incompressible viscous fluid flow between two parallel infinite disks which are located at a distance h(t*) at time t* has been studied. The upper disk moves towards the lower disk with velocity h'(t*). The lower disk is porous and rotates with angular velocity Omega(t*). A magnetic field B(t*) is applied perpendicular to the two disks. It has been found that the governing Navier-Stokes equations reduce to a set of ordinary differential equations if h(t*), a(t*) and B(t*) vary with time t* in a particular manner, i.e. h(t*) = H(1 - alpha t*)(1/2), Omega(t*) = Omega(0)(1 - alpha t*)(-1), B(t*) = B-0(1 - alpha t*)(-1/2). These ordinary differential equations have been solved numerically using a shooting method. For small Reynolds numbers, analytical solutions have been obtained using a regular perturbation technique. The effects of squeeze Reynolds numbers, Hartmann number and rotation of the disk on the flow pattern, normal force or load and torque have been studied in detail

Free Energy Gap Dependence of the Electron-Transfer Rate from the Inverted to the Normal Region

numerical study of the free energy gap (FEG) dependence of the electron-transfer rate in polar solvents is presented. This study is based on the generalized multidimensional hybrid model, which not only includes the solvent polarization and the molecular vibration modes, but also the biphasic polar response of the solvent. The free energy gap dependence is found to be sensitive to several factors, including the solvent relaxation rate, the electronic coupling between the surfaces, the frequency of the high-frequency quantum vibrational mode, and the magnitude of the solvent reorganization energy. It is shown that in some cases solvent relaxation can play an important role even in the Marcus normal regime. The minimal hybrid model involves a large number of parameters, giving rise to a diverse non-Marcus FEG behavior which is often determined collectively by these parameters. The model gives the linear free energy gap dependence of the logarithmic rate over a substantial range of FEG, spanning from the normal to the inverted regime. However, even for favorable values of the relevant parameters, a linear free energy gap dependence of the rate could be obtained only over a range of 5000-6000 cm(-1) (compared to the experimentally observed range of 10000 cm(-1) reported by Benniston et al.). The present work suggests several extensions/generalizations of the hybrid model which might be necessary to fully understand the observed free energy gap dependence.

Zero-bias conductance and energy gap measurements in LaNiO3-YBa2Cu3O7-x junctions

Conductance measurements of junctions between a high- superconductor and a metallic oxide have been carried out along the a-b plane to examine the tunnel-junction spectra. For these measurements, in situ films have been grown on c-axis oriented thin films using the pulsed laser deposition technique. Two distinctive energy gaps have been observed along with conductance peaks around zero bias. The analysis of zero-bias conductance and energy gap data suggests the presence of midgap states located at the centre of a finite energy gap. The results obtained are also in accordance with the d-wave nature of high- superconductors.

Flow of metal into the flash gap in the last stages of a plane-strain closed-die forging operation

In closed-die forging the flash geometry should be such as to ensure that the cavity is completely filled just as the two dies come into contact at the parting plane. If metal is caused to extrude through the flash gap as the dies approach the point of contact — a practice generally resorted to as a means of ensuring complete filling — dies are unnecessarily stressed in a high-stress regime (as the flash is quite thin and possibly cooled by then), which reduces the die life and unnecessarily increases the energy requirement of the operation. It is therefore necessary to carefully determine the dimensions of the flash land and flash thickness — the two parameters, apart from friction at the land, which control the lateral flow. The dimensions should be such that the flow into the longitudinal cavity is controlled throughout the operation, ensuring complete filling just as the dies touch at the parting plane. The design of the flash must be related to the shape and size of the forging cavity as the control of flow has to be exercised throughout the operation: it is possible to do this if the mechanics of how the lateral extrusion into the flash takes place is understood for specific cavity shapes and sizes. The work reported here is part of an ongoing programme investigating flow in closed-die forging. A simple closed shape (no longitudinal flow) which may correspond to the last stages of a real forging operation is analysed using the stress equilibrium approach. Metal from the cavity (flange) flows into the flash by shearing in the cavity in one of the three modes considered here: for a given cavity the mode with the least energy requirement is assumed to be the most realistic. On this basis a map has been developed which, given the depth and width of the cavity as well as the flash thickness, will tell the designer of the most likely mode (of the three modes considered) in which metal in the cavity will shear and then flow into the flash gap. The results of limited set of experiments, reported herein, validate this method of selecting the optimum model of flow into the flash gap.

Firing characteristics of a simple coaxial triggeredva cuum gap

The firing and delay characteristics of a simple coaxial type of triggered vacuum gap (TVG) are described and compared with the planar type. The designs are new and differ from those reported earlier. By analogy with gaseous breakdown the statistical and formative time lags have been determined.

An elementary approach to gap theorems

Using elementary comparison geometry, we prove: Let (M, g) be a simply-connected complete Riemannian manifold of dimension >= 3. Suppose that the sectional curvature K satisfies -1-s(r) <= K <= -1, where r denotes distance to a fixed point in M. If lim(r ->infinity) e(2r) s(r) = 0, then (M, g) has to be isometric to H-n.The same proof also yields that if K satisfies -s(r) <= K <= 0 where lim(r ->infinity) r(2) s(r) = 0, then (M, g) is isometric to R-n, a result due to Greene and Wu.Our second result is a local one: Let (M, g) be any Riemannian manifold. For a E R, if K < a on a geodesic ball Bp (R) in M and K = a on partial derivative B-p (R), then K = a on B-p (R).

Delay time of a vacuum gap triggered by an exploding wire

The experimental results of delay time of a vacuum gap triggered by an exploding wire plasma have been reported. It consists of explosion delay time and propagation delay time. The explosion delay time has been found to be dependent on the parameters of the exploding wire and the exploding wire circuit and is independent of vacuum gap configuration. The propagation delay time depends on the properties of the exploding wire plasma and vacuum gap parameters such as the number of injection slots, gap spacing, gap polarity, etc. In the absence of prebreakdown current in the vacuum gap, the breakdown can be initiated only after the plasma completely bridges the gap spacing. Under this specific condition, it has been shown that the delay time data can be used to calculate the plasma velocity.

Self-excited triggered vacuum gap

The self-triggering action of the TVG under DC conditions using the same power source as the main circuit is described. Because of the low impedance of the power source compared with the thyratron pulse generator, the TVG can be triggered with voltages as low as 85 V. It is found that circuit conditions influence the minimum stable arc currents that can be sustained.

Enhancement of the Peierls gap by a radiation field

The stability of the Peierls phase is investigated in the presence of a radiation with frequency less than that for inter-band transitions. It is observed that such an external radiation enhances the gap. This result is in contrast with the case when the external radiation has a frequency higher than that for inter-band transitions.

A simple triggered vacuum gap

A simple triggered vacuum gap has previously been described by the authors in this journal (see ibid., vol.5, 415, 1972). Further studies have resulted in improvement of the performance with regard to sensitivity and consistency of the trigger characteristics and immunity from bridging due to metal particles eroded from the arc. The earlier design suffered from rather frequent bridging of the auxiliary gap and showed rather wide scatter in its trigger characteristics. In the present design thermally stable materials like fused quartz, machinable ceramic 'Supramica 500' (Mycalex Corporation of America), lead titanate, barium titanate (LCC HTD) and silicon carbide have been used to insulate the trigger electrode from the cathode. Consistent triggerings free from bridging, at relatively low voltages of 200-400 V have been obtained.

Delay characteristics of a simple triggered vacuum gap

Firing delays of a simple triggered vacuum gap are reported in this paper. The effects of insulating materials in the auxiliary gap, auxiliary gap current, main gap current and electrode separation on the delay have been investigated. The presence of insulating material in the auxiliary gap having low auxiliary gap resistance appears to exhibit large delay. Delay decreases considerably with increase of current in the auxiliary and the main gaps, but it increases with increase of electrode separation. The scatter in the delay is less than 25 ps and 500 ps with supramica (Mycalex Corporation of America) and silicon carbide respectively at lower values of auxiliary gap current and it becomes negligible for supramica at auxiliary gap currents greater than 6A. This investigation appears to indicate that the simple device can be used as a fast switch.

Low-voltage and high-current delay characteristics of a simple triggered vacuum gap

Low-voltage and high-current switching delay characteristics of a simple triggered vacuum gap (TVG) are described using lead zirconate titanate as the dielectric material in the auxiliary gap. This TVG has superior performance at high currents (up to 14 kA was studied) with regard to delay, reliable firing and extended life as compared to the one using either supramica or silicon carbide. The total delay consists of three intervals: to break down the auxiliary gap, to propagate the trigger plasma and to break down the main gap. The data on the influence of the various parameters like the trigger voltage, current, energy and the main circuit energy are given. It has been found that the delay due to the first two intervals is small compared to the third.

Landau-Zener problem with waiting at the minimum gap and related quench dynamics of a many-body system

We discuss a technique for solving the Landau-Zener (LZ) problem of finding the probability of excitation in a two-level system. The idea of time reversal for the Schrodinger equation is employed to obtain the state reached at the final time and hence the excitation probability. Using this method, which can reproduce the well-known expression for the LZ transition probability, we solve a variant of the LZ problem, which involves waiting at the minimum gap for a time t(w); we find an exact expression for the excitation probability as a function of t(w). We provide numerical results to support our analytical expressions. We then discuss the problem of waiting at the quantum critical point of a many-body system and calculate the residual energy generated by the time-dependent Hamiltonian. Finally, we discuss possible experimental realizations of this work.